Added meshes will not be aligned with the current transform orientation
After selecting your 'local coordinate' object, go to Edit Mode and select a face the represents your 'floor' rotation. Shift Numpad 7 will let you align your view to the Top view of this face, and in Object mode add your new object - and in the F6 panel/ tool bar operator panel, check 'align to view' and the new object should be aligned to your 'local coordinate' object.